The current default appearance of an “Update Available” notification looks like this on my systems (Home Assistant Supervised and Home Assistant OS):
I took a look at a terciary system I’ve not touched in a while and found this : -
This seems consistent with what Taras just posted too.
And it’s a system running on a Pi3 from SD running HA OS
So I’m not quite sure where this ‘apparent’ myth regarding
"auto-updating" comes from ???
Go to the System tab on that screen and take a look at what the Supervisor says for version and latest version.
Er !
That’s exactly what these images show, installed version vs latest version ???
The ‘system’ view, just shows the supervisor versioning and the host system versioning.
I have upgraded all my systems now apart from the production machine.
When you upgrade HA OS it’s only reasonable that it updates the supervisor at the same time as its part of the same package.
I’m on supervisor 229 at the moment so I’ll monitor that going forward and see it that ever jumps the gun 
This is it right here - the supervisor updates automatically, independently of the OS and Home Assistant. For example, last week mine went from 228 to 229 automatically. I’ll add that occasionally a supervisor update will show up in the Dashboard tab in your screenshot alongside Home Assistant and the OS, but if you don’t take action on it it will update on its own.
Okay I’ll keep an eye out for that (but as I said updating HA OS implicitly implies an upgrade to the current latest supervisor, so I can only watch for this on only ‘one’ of my instances).
I’m not aware of anyone complaining of breaking changes to the supervisor though and though @finity specifically stated 'supervisor' and I had assumed (apologies finity) HA release (as that’s where all the breaking changes come from in my limited experience).
You know what they say about assumptions 
Yeah, there aren’t breaking changes in the supervisor per se, but there have been issues in the past where people have had a supervisor auto-upgrade go bad and not be able to fix it right away if they aren’t at home. Like any upgrade, there’s just a degree of risk inherent in the upgrade process itself (not a high risk level I’d say, but risk nonetheless).
And to complete the message, devs never published instructions about how to recover the system in safe way. The only way was hard reboot which was not confirmed to be the way. (for at least one person it turned into the need of reinstalling the system)
Or needing to try to roll back the supervisor version manually.
But even then as soon as the system realized that you were on the old supervisor it did the auto-update thing again and broke it all over again because you have literally zero control over that functionality.
What is the Last releases for docker ha Supervisor?